The model is defined as a so called S-system model. The S-system formalism (Savageau 1976, Voit 2000) is based on approximating kinetic laws with multivariate power-law functions. A model consists of n non-linear ODEs and the generic form of equation i reads
Xi'(t) = αi ∏j=1..n Xj(t)gij - βi ∏j=1..n Xj(t)hij
where X is a vector (length n) of dependent variables, α and β are vectors (length n) of non-negative rate constants and g and h are matrices (n*n) of kinetic orders, that can be negative as well as positive.
The system was introduced by Maki et al. (2001) and applied in Kimura et al. (2005) and Kutalik et al. (2007). It represents a genetic network with 30 variables. A positive regulation is indicated by a black arrow, whereas a negative regulation is indicated by a red arrow.
The parameters are:
| for all i: αi=1 | ||||
| for all i: βi=1 | ||||
| g1,14=-0.1 | g5,1=1.0 | g6,1=1.0 | g7,2=0.5 | g7,3=0.4 |
| g8,4=0.2 | g8,17=-0.2 | g9,5=1.0 | g9,6=-0.1 | g10,7=0.3 |
| g11,4=0.4 | g11,7=-0.2 | g11,12=0.4 | g12,16=0.5 | g13,8=0.6 |
| g14,9=1.0 | g15,10=0.2 | g16,11=0.5 | g16,22=-0.2 | g17,13=0.5 |
| g19,14=0.1 | g20,15=0.7 | g20,26=0.3 | g21,16=0.6 | g22,23=0.1 |
| g23,17=0.2 | g24,15=-0.2 | g24,18=-0.1 | g24,19=0.3 | g25,20=0.4 |
| g26,21=-0.2 | g26,28=0.1 | g27,24=0.6 | g27,25=0.3 | g27,30=-0.2 |
| g28,25=0.5 | g29,26=0.4 | g30,27=0.6 | other gij=0.0 | |
| for all i: hii=1.0, other hij=0 | ||||
The ODE of X1 according to Eq. 1: X1'(t) = 1-1*X1(t)*(X14(t))-0.1.
The system specification in the same format as the problem: ss_30genes.
The system specification in SBML format: ss_30genes.xml.
A simple Matlab script for simulating the system is given in ss_30genes.m.
Problem ss_30genes1 is similar to problem ss_30genes2 presented in Kimura et al. (2005). The difference is that fewer experiments are used and that no noise is added in this problem.
Problem ss_30genes2 is presented in Kimura et al. (2005).
Problem ss_30genes3 is presented in Liu and Wang (2008).
Problem pe_ss_30genes2 is the same as ss_30genes2 but with a fixed structure, i.e. a parameter estimation problem.
Problem pe_ss_30genes2f is the same as pe_ss_30genes2 but with fixed initial point for each variable in each time-series.
Kimura,S., Ide,K., Kashihara,A., Kano,M., Hatakeyama,M., Masui,R., Nakagawa,N., Yokoyama,S., Kuramitsu,S., Konagaya,A. (2005) Inference of S-system models of genetic networks using a cooperative coevolutionary algorithm. Bioinformatics, 21, 1154-63. PMID:15514004
Kutalik,Z., Tucker,W., Moulton,V. (2007) S-system parameter estimation for noisy metabolic profiles using newton-flow analysis. IET Syst Biol., 1, 174-80. PMID:17591176
Liu,P.K., Wang,F.S. (2008) Inference of biochemical network models in S-system using multiobjective optimization approach. Bioinformatics, 24, 1085-92. PMID:18321886
Maki,Y., Tominaga,D.,Okamoto,M., Watanabe,S., Eguchi,Y. (2001) Development of a system for the inference of large scale genetic networks. Pac Symp Biocomput. 2001, 446-58. PMID:11262963
Savageau,M.A. (1976) Biochemical systems analysis: a study of function and design in molecular biology (Addison-Wesley, Reading, Mass).
Voit,E.O. (2000) Computational analysis of biochemical systems. A practical guide for biochemists and molecular biologists. Cambridge University Press, Cambridge, 176-184.